A full$-$depth asphalt pavement will be placed on a subgrade with an effective roadbed resilient modulus of $10,000$ psi. Assuming a layer coefficient of $0\mathrm{.}44$ for the asphalt layer, a drop in PSI from $4\mathrm{.}2$ to $2\mathrm{.}5,$ an overall standard deviation of $0\mathrm{.}5,$ a predicted ESAL of $30,000,000,$ and a reliability of $90\%.$ Determine the required SN and the thickness of the asphalt layer using the AASHTO methodology.